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9231 P41 - Jun 2021 - Q1 - 7 marks
6791

A random sample of 7 observations of a variable \(X\) are as follows.

8.267.787.928.048.277.958.34

The population mean of \(X\) is \(\mu\).
(a) Test, at the \(10 \%\) significance level, the null hypothesis \(\mu=8.22\) against the alternative hypothesis \(\mu\lt 8.22\).
(b) State an assumption necessary for the test in part (a) to be valid.

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